NEWS
Intensive Lecture Series by Specially Appointed Visiting Professor Tadashi Tokieda
Update: June 25, 2026
On June 15, 16, and 17, 2026, a series of intensive lectures titled "Riyoshiyo Ryoshirikigaku (Let's Use Quantum Mechanics)" was held at the Troyer Memorial Arts and Sciences Hall by Specially Appointed Visiting Professor Tadashi Tokieda, Professor of Mathematics at Stanford University. Professor Tokieda specializes in topology and mathematical physics and is internationally known for his distinctive approach to mathematics and physics education, emphasizing "thinking with your hands." This series followed last winter's highly acclaimed three-part lecture series--"A World from a Sheet of Paper," "Computation Without Numbers or Equations," and "Cut-and-Paste Magic Show"--and marked the first four-part series offered in early summer.
The lectures were moderated by Associate Professor Takashi Kaburagi. Approximately 120 students, faculty, and staff attended each session, including students enrolled in Introduction to Computer Science as well as participants joining online.
The theme of this series was not to learn quantum mechanics, but to use quantum mechanics. This year marks the 100th anniversary of the discovery of quantum mechanics. Countless technologies that underpin modern daily life--including semiconductors, medical technologies, and nuclear energy--are founded on quantum mechanics. Yet understanding and mastering the subject still requires extensive specialized knowledge, making it an inaccessible field for many people.
Professor Tokieda presented an approach centered on three fundamental ideas underlying quantum mechanics: (1) dimensional analysis using Planck's constant, (2) estimating confinement energy through Heisenberg's uncertainty principle, and (3) making effective use of potentials. By combining these concepts, he demonstrated how one can estimate answers without relying on specialized knowledge or solving complicated equations. As an introduction to this approach, Professor Tokieda introduced Fermi estimation. A classic example is the seemingly impossible question, "How many piano tuners are there in Chicago, USA?" By successively estimating quantities such as the number of households, the total number of pianos, and the annual frequency of piano tuning, one can arrive at a reasonable approximation without conducting a detailed survey. This style of reasoning is also well known for appearing in consulting and IT company job interviews. During the lectures, Professor Tokieda showed how augmenting Fermi estimation with the three key ideas from quantum mechanics makes it possible to accurately estimate an astonishingly wide range of phenomena--from familiar everyday quantities such as the calories in a single bite of a candy or annual rainfall, to microscopic quantities such as the atomic radius of hydrogen and the bond energy of water, and even cosmic-scale phenomena such as the radius of a neutron star and the entropy of a black hole.
Participating students shared the following comments:
- I was surprised by the explanation that the calories in living organisms can be estimated from the composition and quantities of CHNOPS molecules. But the more I thought about it, the more it made sense: after all, food is ultimately made of matter, so it is reasonable that its energy content can be calculated from its physical properties.
- The question that fascinated me was why droplets hanging around us are all about the same size. [...] Watching the calculation that derives their size from familiar forces such as gravity and surface tension made me realize that every ordinary scene we casually overlook has a clear physical explanation behind it. Even as a humanities student, the lecture gave me a fresh sense that the everyday world had suddenly become much sharper and more meaningful.
- I had assumed that understanding energy levels required difficult calculations like solving the Schr?dinger equation. Instead, Professor Tokieda never solved it at all. Using only the simple, visual condition that "the wave fits perfectly," he effortlessly derived the energy levels. What impressed me most was seeing the power of changing one's perspective and reducing a seemingly intractable problem to its essential simplicity, rather than confronting it head-on with complicated calculations.
- The estimate that a 50g piece of candy has about 10^6 joules, which is around 240 kcal, made the idea feel more concrete. This example stuck with me because I didn't really need a full understanding of physics to understand. It showed me that rough estimation is useful not just for solving textbook problems, but also for making sense of things we encounter in daily life.
- I found it fascinating how simple estimations could immediately produce realistic values, such as annual rainfall. The method of deriving essential numerical values from only a few variables and then validating them by comparing them with observed data reminded me of the way models are built in data science.
